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%I #15 Nov 18 2020 09:32:20
%S 1,1,2,4,2,18,4,2,80,34,4,2,482,196,36,4,2,3280,1418,292,44,4,2,26244,
%T 11292,2426,304,48,4,2,231148,106132,22156,3010,372,56,4,2,2320130,
%U 1046176,225804,32308,3892,424,60,4,2,25238348,11679626,2585080,366484,42176,4540,472,68,4,2
%N Number T(n,k) of permutations of [n] having exactly k consecutive 3-term arithmetic progressions; triangle T(n,k), n>=0, 0<=k<=max(n-2,0), read by rows.
%H Alois P. Heinz, <a href="/A295390/b295390.txt">Rows n = 0..18, flattened</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Arithmetic_progression">Arithmetic progression</a>
%H <a href="/index/No#non_averaging">Index entries related to non-averaging sequences</a>
%e Triangle T(n,k) begins:
%e 1;
%e 1;
%e 2;
%e 4, 2;
%e 18, 4, 2;
%e 80, 34, 4, 2;
%e 482, 196, 36, 4, 2;
%e 3280, 1418, 292, 44, 4, 2;
%e 26244, 11292, 2426, 304, 48, 4, 2;
%e 231148, 106132, 22156, 3010, 372, 56, 4, 2;
%e 2320130, 1046176, 225804, 32308, 3892, 424, 60, 4, 2;
%e ...
%Y Column k=0 gives A295370.
%Y Row sums give A000142.
%Y Cf. A162982, A289207.
%K nonn,tabf
%O 0,3
%A _Alois P. Heinz_, Nov 21 2017
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